Exponential stability of impulsive stochastic functional differential equations

In this paper, we investigate the pth moment and almost sure exponential stability of impulsive stochastic functional differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Meanwhile, an example and simulations are given to show that impulses play an important role in pth moment and almost sure exponential stability of stochastic functional differential equations with finite delay.     

L-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem

In this paper, the parabolic quasi-variational inequalities are transformed into a noncoercive elliptic quasi-variational inequalities. A new iterative discrete algorithm is proposed to show the existence and uniqueness, and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation. The proposed approach stands on a discrete L^∞-stability property with respect to the right-hand side and obstacle defined as an impulse control problem.     

Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order

In this paper, we prove the existence and uniqueness of solutions for an anti-periodic boundary value problem of nonlinear impulsive differential equations of fractional order α∈(2,3] by applying some well-known fixed point theorems. Some examples are presented to illustrate the main results.     

基于蒙特卡洛法的水下无线光传输特性分析

水下无线光传输面临功率衰减和时域宽度变大的问题,蓝绿光长距离传输特性更难以测试。利用蒙特卡洛法对水下蓝绿高斯光束传输过程进行仿真,分析海水类型、传输距离和发散角等因素对接收功率及脉冲响应的影响,数值对比小发散角情况下不同海水类型和传输距离的接收面上功率分布。结果表明,随着海水衰减系数、传输距离和发散角的增加,接收功率逐渐减小,时域宽度扩展变大。其中浑浊港湾海水在10 m以上传输距离时,接收功率受发散角的影响微乎其微,而时域宽度随发散角的增加由0.32 ns变为0.8 ns。虽然传输距离相差一倍,纯海水和清澈海水功率相似度依然高达99%。基于海水衰减系数的差异性,利用功率相似度和面积比来研究水下长距离的传输,可高效快速地获得长距离传输特性。     

Double Solutions of Impulsive Dynamic Boundary Value Problems on a Time Scale

A double fixed-point theorem is applied to obtain the existence of at least two positive solutions of a right focal boundary value problem for a second order impulsive dynamic equation on a time scale.     

A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions

This paper considers a class of optimal control problems that allows jumps in the state variable. We present the necessary optimality conditions of the Impulse Control Maximum Principle based on the current value formulation. By reviewing the existing impulse control models in the literature, we point out that meaningful problems do not satisfy the sufficiency conditions. In particular, such problems either have a concave cost function, contain a fixed cost, or have a control-state interaction, which have in common that they each violate the concavity hypotheses used in the sufficiency theorem. The implication is that the corresponding problem in principle has multiple solutions that satisfy the necessary optimality conditions. Moreover, we argue that problems with fixed cost do not satisfy the conditions under which the necessary optimality conditions can be applied. However, we design a transformation, which ensures that the application of the Impulse Control Maximum Principle still provides the optimal solution. Finally, we show for the first time that for some existing models in the literature no optimal solution exists.     

具高阶Laplace算子的非线性脉冲时滞双曲型方程的振动判据

研究一类具高阶Laplace算子的非线性脉冲时滞双曲型偏微分方程的振动性,利用特征函数法和一阶脉冲时滞微分不等式,获得了该类方程在两类不同边值条件下所有解振动的若干充分性判据.所得结论充分反映了脉冲和时滞在振动中的影响作用.     

脉冲响应法测量混响时间技术的研究

本文介绍了一种根据厅堂脉冲响应特性,利用计算机数字信号处理技术,迅速,准确地测量混响时间的实现方法。     

Dynamic programming for multidimensional stochastic control problems

In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem, singular control problem and impulse control problem as special cases. Using a unified treatment of dynamic programming, we show that the value function of the problem is a viscosity solution of certain Hamilton-Jacobi-Bellman (HJB) quasivariational inequality. The uniqueness of such a quasi-variational inequality is proved. Supported in part by USA Office of Naval Research grant #N00014-96-1-0262. Supported in part by the NSFC Grant #79790130, the National Distinguished Youth Science Foundation of China Grant #19725106 and the Chinese Education Ministry Science Foundation.     

Impulse coefficient for square grounding grids in low resistivity soils: Influence of injection electrode

Impulse coefficient is calculated, for the first time, by considering the response of the current injection electrode connected to ground grids for lightning subsequent return strokes. It is observed that the impulse coefficient can be substantially amplified specially for low resistivity soils (e.g. forest grounds) and the enlargement is a function of the length of the injection electrode. Several rigorous finite-difference time-domain (FDTD)-based simulations have been performed and a new semi-empirical formula for impulse coefficient, which takes into account the injection electrode's length, is provided. The proposed expression is verified experimentally.